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A Critical Point for Random Graphs with a Given Degree Sequence
TLDR
It is shown that if Σ i(i - 2)λi > 0, then such graphs almost surely have a giant component, while if λ0, λ1… which sum to 1, then almost surely all components in such graphs are small.
Graph Colouring and the Probabilistic Method
  • B. Reed
  • Computer Science
  • 20 November 2001
TLDR
This talk defines graph colouring, explains the probabilistic tools which are used to solve them, and why one would expect the type of tools used to be effective for solving the types of problems typically studied.
The Size of the Giant Component of a Random Graph with a Given Degree Sequence
TLDR
The size of the giant component in the former case, and the structure of the graph formed by deleting that component is analyzed, which is basically that of a random graph with n′=n−∣C∣ vertices, and with λ′in′ of them of degree i.
Mick gets some (the odds are on his side) (satisfiability)
TLDR
The authors present a linear-time algorithm that satisfies F with probability 1-o(1) whenever c<(0.25)2/sup k//k and establish a threshold for 2-SAT: if k = 2 then F is satisfiable with probability1-o (1) Whenever c<1 and unsatisfiable with probabilities 1-O(1), whenever c>1.
A Bound on the Strong Chromatic Index of a Graph,
We show that the strong chromatic index of a graph with maximum degree�; is at most (2��)�2, for some�>0. This answers a question of Erdo�s and Ne�et�il.
Finding odd cycle transversals
Further algorithmic aspects of the local lemma
TLDR
This is the author's version of the work and it is posted here by permission of ACM for your personal use.
Acyclic Coloring of Graphs
TLDR
It is shown that if G has maximum degree d, then A(G) = 0(d4/3) as d → ∞, which settles a problem of Erdos who conjectured, in 1976, that A( G) = o(d2) as d →∞.
Minima in branching random walks
Given a branching random walk, let $M_n$ be the minimum position of any member of the $n$th generation. We calculate $\\mathbfEM_n$ to within O(1) and prove exponential tail bounds for
The height of a random binary search tree
  • B. Reed
  • Computer Science
    JACM
  • 1 May 2003
TLDR
It is shown that there exist constants α = 4.311… and β = 1.953 such that E(H<inf>n</inf></i) = α<i>ln n</i> − β(i) ln n + O(1), and thatVar(H) = <i>O</i>(1), which indicates the height of a random binary search tree on H(n) nodes.
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